Initializes and sets up reference elements and physical meshes for DG.
Author jlchan
20 Stars
Updated Last
1 Year Ago
Started In
August 2020


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Routines to initialize reference element operators, physical mesh arrays, and connectivity for nodal discontinuous Galerkin (DG) methods. Codes roughly based on Nodal Discontinuous Galerkin Methods by Hesthaven and Warburton (2007). The original port from Matlab to Julia was by Yimin Lin, with subsequent modifications by Jesse Chan.

This package is registered and can be installed via ] add StartUpDG.

Usage overview

Variables are contained within structs rd::RefElemData and md::MeshData, which contain quantities from Globals1D, Globals2D, Globals3D in the Nodal DG book codes. These can be used to compute DG derivatives, and are useful for matrix-free implementations of DG methods using explicit time-stepping.

using StartUpDG

# polynomial degree and mesh size
N = 3
K1D = 8

# init ref element and mesh
rd = RefElemData(Tri(), N)
VXY, EToV = uniform_mesh(Tri(), K1D)
md = MeshData(VXY, EToV, rd)

# Define a function by interpolation
(; x, y) = md
u = @. 2 + .5*exp(-100*(x^2 + y^2))

# Compute derivatives using geometric mapping + chain rule
(; Dr, Ds) = rd
(; rxJ, sxJ, J) = md
dudx = (rxJ .* (Dr*u) + sxJ .* (Ds*u)) ./ J